Method and device for determining positions of objects

ABSTRACT

As equipment has a transducer (G) that receives signals from a number of objects with unknown positions and senses the directions from the transducer to the objects. The directions of the sight lines to the objects are sensed in at least two separate transducer locations. The transducer signals are supplied to calculator (CU) which calculates the positions of the objects.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of determining the position ofobjects in equipment comprising at least one transducer designed toreceive signals from a set of objects arranged to emit signals thatpropagate linearly between the objects and the transducer, and membersarranged to produce direction-defining signals that define the directionof the sight lines from the transducer to the objects in relation to thetransducer.

The invention also relates to an arrangement for creating a set ofobjects with known positions for equipment of the above type.

2. Description of the Related Art

The following terms are used in this application:

the location of an object is defined by the position and/or orientationof the object;

the position of an object is determined by a number of translationcoordinates;

the orientation of an object is determined by a number of rotationalcoordinates.

Furthermore, the term object denotes an object able to emit signals thatcan be received by the transducer, that is to say signals that propagatelinearly between the object and the transducer. Such signals areprimarily optical signals with frequencies within the visible wavelengthrange or outside this range, such as infrared light. Examples of objectsare light sources (e.g. light bulbs or light-emitting diodes),reflectors (e.g. markers of reflecting tape) or details of thetransducer's surroundings identifiable by means of image analysis (e.g.corners, holes, light points or markers having a certain shape and witha colour or brightness that deviates from the surroundings).Alternatively other signal forms may be used, e.g. ultrasonic ormicrowave signals, in which case the objects, for instance, consist ofsources or reflectors for these signals, for instance.

A position transducer arrangement is known through the Swedish patentspecification No. 444 530. This arrangement preferably utilizes opticalsignals. An optical transducer is designed to sense the direction fromthe transducer to each of a number of light sources, whose positions inrelation to each other are known. The transducer determines thedirections to at least three such light sources. The arrangement hascalculation means which, on the basis of the directions thus determined,determine the angles between the sight lines from the transducer to thelight sources and which, on the basis of these directions and angles andof the known positions of the light sources in relation to each other,calculate the transducer's position and possibly also its orientation inrelation to the light sources.

A position transducer arrangement operating in accordance with a similarprinciple is known through Swedish patent specification No. 458 427. Itstransducer consists of a device that generates a two-dimensional imageof its surroundings. An image-analysis system receives the informationcontent of the image and scans the image for a number--at leastthree--of recognizable, predetermined details in the surroundings havingknown positions in relation to each other. The image analysis systemdetermines the position of the details in the image. The arrangementalso includes calculation means that, from the positions of the detailsin the image, determine the directions of the sight lines from thetransducer to the details, from the directions determine the anglesbetween the sight lines and, on the basis of these directions and anglesand of the known relative positions of the details, calculate theposition of the transducer and possibly also its orientation in relationto the details.

The older Swedish patent application No. 9403255-4 describes a controlequipment utilizing a control device carried by an operator, e.g. in theform of a free handle. The control device has a transducer operating onthe same principle as the transducers described in the two precedingparagraphs. With the aid of the transducer the directions are determinedto a number of objects (e.g. light sources, markers or detailsidentifiable in the surroundings by image analysis) with known relativepositions. The equipment also has means which, on the basis of thedirections thus determined, calculate the angles between the sight linesto the object and which, on the basis of these directions and angles andof the known positions of the objects, determine the position of thecontrol device and possibly also its orientation in relation to theobjects.

Equipment of the type described above requires that the transduceralways has at least three objects with known positions within its fieldof vision (four objects are required for some configurations). A typicaltransducer of this type has a certain working range within which it canalter location, i.e. position and/or orientation during use. To ensurethat the transducer always has a sufficient number of suitablypositioned objects within its field of vision, regardless of its actuallocation in the working range, therefore, more than three objects aregenerally required, and if the working range is large a relatively largenumber of objects is required. The relative positions of these objectsmust be known with great accuracy. The positions of the objects musttherefore be measured both when the equipment is commissioned and if theworking range is to be extended or altered.

Known measuring methods employing distance and/or angle measurement,triangulation or the like have hitherto been used to determine thepositions of objects in equipment of the type in question. Determinationof the positions to the high degree of accuracy required demands specialequipment, e.g. theodolites, and expert knowledge, as well as beingcomplicated and time-consuming. These circumstances have generallyentailed a considerable practical and economic drawback.

SUMMARY OF THE INVENTION

The object of the invention is to provide a method and arrangement thatenable a set of objects to be created quickly and simply, and withoutspecial equipment, or with a minimum of such equipment, with accuratelyknown positions, for use in equipment of the type described in thepreamble.

The characteristic features of a method and arrangement according to theinvention are revealed in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in more detail in the following withreference to the accompanying FIGS. 1-5.

FIG. 1a shows coordinate systems and designations for a simplified casewith one object and two transducer locations.

FIG. 1b shows the same magnitudes for the more general case with anarbitrary number of transducer locations.

FIG. 1c shows schematically an arrangement for performing the methodaccording to the invention.

FIG. 2a reveals an example of the measuring procedure according to theinvention, in the form of a flow chart.

FIG. 2b shows a flow chart of the calculations made during thedetermination process.

FIG. 2c illustrates an alternative procedure of determination.

FIG. 3a shows a portable frame according to the invention, withreference markers.

FIG. 3b shows in more detail an example of such a frame.

FIGS. 3c and 3d show examples of the markers'shape in the frameaccording to FIG. 3b.

FIG. 4a shows how a beam with two transducer locations can be used inthe method according to the invention.

FIG. 4b shows a hand-held transducer unit with two sensors.

FIG. 5 illustrates how objects with already determined positions in canbe used for determining the positions of new objects when extending theworking range of the transducer equipment.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1a shows some of the magnitudes used in the method according to theinvention in an assumed simplified case with two separate transducerlocations. A transducer G is shown in two locations P₁ and P₂, known inrelation to each other. The transducer may be of the type described inthe publications mentioned above. In its upper part as shown in theFigure it has a wide-angle lens 11, whose field of vision is thusdirected substantially upwards in the Figure. In the example shown inFIG. 1 the transducer is designed to be hand-held and its lower part istherefore in the form of a handle 12. The positions of the twotransducer locations are described in an orthogonal coordinate systemwith origo O and the axes x, y, z by the vectors

v₀₁ =(x₀₁, y₀₁, z₀₁)

v₀₂ =(x₀₂, y₀₂, z₀₂)

The orientations of the two transducer locations are also assumed to beknown in the coordinate system x-y-z. Each transducer location can thusbe described by a six-dimensional vector.

The two transducer locations--including both position andorientation--can be determined by measurement against objects with knownpositions in the manner described in the above publications. The twotransducer locations thus become known in the coordinate system of theknown objects and thus also in relation to each other. Alternatively, aswill be described in more detail in the following, the two transducerlocations may be defined by arranging two transducer locations connectedtogether mechanically in such a way that the two transducer locationsbecome mechanically fixed and known in relation to each other. The twotransducer locations will then be defined in a coordinate system that isfixed in relation to the mechanical system. This coordinate system isthen assumed to be the one shown in FIG. 1.

In the manner described in the above-mentioned publications thetransducer in transducer location P₁ determines the direction of thesight line SL₁ from the transducer to an object with the as yet unknownposition Q₁. The position of the object based on this determination canfor the moment be described by a vector

v₁₁ =v₀₁ +t₁₁ k₁₁

where

t₁₁ is an unknown parameter

k₁₁ =(α₁₁, β₁₁, γ₁₁) is a unit vector in the direction of the sight linecalculated partly from the orientation of the transducer and partly fromthe direction of the sight line in the coordinate system of thetransducer.

The vector v₁₁ has the components

x₁₁ =x₀₁ +t₁₁ α₁₁

y₁₁ =y₀₁ +t₁₁ β₁₁

z₁₁ =z₀₁ +t₁₁ γ₁₁

Correspondingly, the direction of the sight line SL₂ from the transducerto the same object is determined in transducer location P₂. The positionof the object based on this measurement is described in the same way bya vector

v₁₂ =v₀₂ +t₁₂ k₁₂

where

t₁₂ is an unknown parameter

k₁₂ =(α₁₂, β₁₂, γ₁₂,) is a unit vector in the direction of the sightline calculated partly from the orientation of the transducer and partlyfrom the direction of the sight line in the coordinate system of thetransducer.

The vector v₁₂ has the components

x₁₂ =x₀₂ +t₁₂ α₁₂

y₁₂ =y₀₂ +t₁₂ β₁₂

z₁₂ =z₀₂ +t₁₂ γ₁₂

Ideally the object is at the intersection point of the two sight lines.This point can be obtained by solution of the equation system

    v.sub.11 =v.sub.12

i.e.

    v.sub.01 +t.sub.11 k.sub.11 =v.sub.02 +t.sub.12 k.sub.11

In the Figure it is assumed that the measurements are exact and that thetwo sight lines intersect each other in the object Q₁. Due tounavoidable measuring errors, however, the two sight lines willgenerally not intersect each other exactly. The most likely position ofthe object can IL-hen be determined in accordance with a suitablecriterion and the position may, for instance, be assumed to lie midwayon the shortest line that can be drawn between any point on one of thesight lines and any point on the other sight line. This position of anobject with the serial number "i", in a group of n objects withpositions to be determined (1≦i≦n) is designated v_(i) in the following.

The various transducer locations are chosen so that they give differentsight lines from the transducer to the objects in question. The accuracyincreases the greater the changes in angle of the sight lines when atransducer is moved from one location to another.

FIG. 1b shows the more general case with an arbitrary number of separatetransducer locations P₁ . . . P_(j) . . . P_(m) where m≧2 and where1≦j≦m. The transducer locations P₁, P_(j) and P_(m) are shown in theFigure. For the sake of simplicity only the measurement to a singleobject in position Q_(i) is shown in the Figure. However, the object isone of n objects in an arbitrarily large group of objects (1≦i≦n). Themeasurement is performed in the same manner to the other objects in thegroup, i.e. the sight lines to each of the objects in the group aredetermined at each transducer location.

The positions of the transducer locations are described by the vectors

v₀₁ =(x₀₁, y₀₁, z₀₁)

v_(0j) =(x_(0j), y_(0j), z_(0j))

v_(0m) =(x_(0m), y_(0m), z_(0m))

In each transducer location P_(j) the transducer determines thedirections of the sight lines to the object in the manner described inthe above publications. The position of the object based on thismeasurement can be described in the same way by a vector

v_(ij) =v_(0j) +t_(ij) k_(ij) with the components

x_(ij) =x_(0j) +t_(ij) α_(ij)

y_(ij) =y_(0j) +t_(ij) β_(ij)

z_(ij) =z_(0j) +t_(ij) γ_(ij)

As described above, the position Q_(i) of the object is described by avector v_(i) with the components x_(i), y_(i), z_(i). An example isdescribed with reference to FIG. 2b, of how the position of the objectcan be determined on the basis of the sight-line directions k_(ij).

FIG. 1c shows schematically an arrangement for performing the methodaccording to the invention. It consists of a transducer G with lens 11and handle 12. The transducer is connected to a calculation unit CU bymeans of a signal channel IL in the form of a cable, for instance, alight conductor or an IR link. The transducer, signal channel andcalculation unit may be designed in any of the ways described in thepublications discussed in the preamble, and the calculation unit maythus consist of a computer programmed to control the measurements, storethe results of the measurements and perform the necessary calculations.Besides the means shown in FIG. 1c, there are additional means fordetermining the transducer locations, e.g. in the form of objects withknown positions in the manner described below. The arrangement may alsoinclude signal sources. These may either constitute objects themselvesor may be arranged to emit optical signals, for instance, towardsobjects in the form of reflectors.

FIG. 2a shows schematically a measuring procedure according to theinvention. The transducer is brought to the first transducer location P₁(block GTP₁), and serial number j is set to j=1. The serial number "i"is set to 1 (block i=1). Thereafter the first object to be measured(block DESO_(i)) is designated (selected). In the next block (DP_(ij)/SSL_(ij)) the transducer equipment then determines the present locationof the transducer, e.g. by means of measurements of known objects in themanner described in the publications described in the preamble, and alsothe direction k_(ij) to the relevant object. The position v_(0j) of thetransducer and the sight-line direction k_(ij) are stored for use in thesubsequent calculation of the position of the object. In the next block(ALL i?) an investigation is performed to see if the directions havebeen determined to all the objects to be measured. If not, the serialnumber "i" is increased by 1 (the block i=i+1) and the next object isdesignated. The procedure just described is then repeated for thisobject. When all objects have been run through, i.e. when i=n, thetransducer is moved to the next transducer location P_(j) (GTP_(j)), theserial number j is set to j+1, and the serial number "i" is again set at1 (the block i=1). The objects to be measured have now been designatedand allocated individual serial numbers "i". The transducer equipmentnow measures the objects one by one as described above for locationP.sub. and stores the transducer position v_(0j) and sight-linedirection k_(ij) for each measurement (block DP_(ij) /SSL_(ij)). Whenall objects have been measured (verified in block i=n?) a decision ismade as to whether all desired transducer locations have been included(block ALL j?). If not, the measuring procedure is repeated for the nexttransducer location. When all desired transducer locations have beenused the transducer equipment calculates the positions of the objects tobe determined on the basis of the stored measured values, and storesthese positions. Calculation and storing is performed in block CSP_(i).

FIG. 2b illustrates the calculation process in the form of a flow chart.The method of least square is used as criterion for determining anobjects'position on the basis of the sight lines measured from thevarious transducer locations to the object, i.e. the object is deemed tohave the position resulting in a minimum of the sum of the squares ofthe distances from the position to the sight lines. When the calculationhas commenced i is set =1, i.e. the calculation is first performed forthe object with serial number 1 and the calculation on the basis of thesight lines determined from the m different transducer locations (m>2).First (block d_(ij)) the distance d_(ij) from an arbitrary point v_(i)=(x_(i) y_(i) z_(i)) is expressed to each of the m sight lines to theobject with serial number i from the m transducer locations with serialnumber j (l≦j≦m). The distances are obtained from ##EQU1## where k_(ij)=(α_(ij) +β_(ij) γ_(ij))

v_(0j) =(x_(0j), y_(0j), z_(0j))

Thereafter the sum S of the squares of the distances d_(ij) is formed inthe block S=Σd_(ij) ² i.e. ##EQU2##

The minimum of this sum with regard to x_(i), y_(i), z_(i) is sought inthe block ##EQU3## i.e. the sum S is differentiated with regard tox_(i), y_(i), z_(i), after which the three differentiated equations areset equal to zero. The equation system thus obtained will be ##EQU4##where α_(ij), β_(ij), γ_(ij), x_(0j), y_(0j) and z_(0j) are known. Theequation system is solved in known manner. The values x_(i), y_(i),z_(i) obtained from the equation system constitute the sought locationof the object since there is obviously a physical minimum for the sum S(and not a maximum).

The position of the object with serial number i obtained in this way isstored in the block STO x_(i), y_(i), z_(i). A check is made in blocki=n? to ensure that the position has been calculated for all n objects.If not, i is set to =i+1 and the calculation is repeated for the nextobject.

The above is a description of how the determination procedure can beperformed by determining the sight-line directions in at least twoseparate transducer locations. In principle it is sufficient with twotransducer locations as long as both positions do not lie along the samesight line to one of the objects for which the position is to bedetermined. However, a larger number of measurements is preferable. Thiscan be achieved, for instance, by varying the position and orientationof the transducer substantially arbitrarily during which the system,preferably automatically and at frequent intervals, (when necessary)determines the location of the transducer and also in each locationdetermines the directions of the sight lines to the objects whosepositions are to be determined. When a sufficient number of measurements(e.g. 100-10,000 measurements) have been performed, the positions of theobjects are calculated using all the measurements taken. The accuracy ofdetermining the positions can thus be substantially improved.

According to an alternative measuring method the transducer can be movedsubstantially continuously (i.e. without stopping in specificlocations). The sight lines to the various objects are then measuredcontinuously. Measuring the sight lines to the reference objects isperformed at suitable intervals and the actual location of thetransducer each time a sight line is measured to a new object isobtained, e.g. by interpolation between the measurements of the sightlines to the reference objects. Such a method is illustrated in FIG. 2c.A transducer G is passed continuously along a path between a firsttransducer location P_(a) and a second transducer location P_(b). Sightlines to a first, a second, a third reference object, and so on, aremeasured at a number of points 1, 2, 3, and so on, along the path. Sightlines to a first, a second, a third, and so on, object in a group of newobjects, with unknown positions are measured at a number of points A, B,C, and so on, along the path. The measurements are preferably performedautomatically and the sight lines to the reference objects are measuredat such frequent intervals that the transducer location at eachmeasurement of the sight line to a new object can be obtained withsufficient accuracy through interpolation.

When a plurality of objects and a plurality of transducer locations areused, it is not certain that all the objects will be visible for alltransducer locations. In this case only information from the transducerlocations from which the object is visible is used to determine theposition of each object. (However, an object must of course be visiblefrom at least two different transducer locations.)

As is clear from the above, a transducer equipment of the type describedin the introduction is used in the method described. Since suchequipment contains calculation means it is suitable also to use thesecalculation means for the calculations required in the procedure todetermined the objects'positions described above. The calculation meansof the transducer equipment preferably consists of a digital processorequipment, suitably programmed. It can then also be programmed toperform the above calculations.

The method described above thus allows a number of objects withpreviously unknown positions to be given determined positions, and theirpositions stored. They can thereafter be used for position-determiningwith the aid of transducer equipment of the type described in theintroduction.

FIG. 3a shows how, according to one embodiment of the invention, a standCF can be used for the location-determining of the transducer whenmeasuring objects with unknown positions in the figure. The stand mayhave a side length of a meter or so, for instance, but its dimensionsmust of course be suitable for the application. It is provided withobjects facing the interior of the stand, in the form of markers M₁ -M₄.The objects whose positions are to be determined are designated OB₁-OB₃. The stand is perforated and as open as possible so as to impedethe view between transducer and objects OB₁ -OB₃ as little as possible.During measurement the transducer G is held inside the stand and movedbetween different locations, the latter being so chosen that at eachlocation the transducer has at least three markers M₁ -M₄ and at leastone of the objects OB₁ -OB₃ within its field of vision simultaneously.The positions of the markers M₁ -M4 in relation to each other are known,thus enabling the transducer equipment in each transducer location, onthe basis of these known positions and the sensed directions to themarkers, to determine the location of the transducer. The positions ofthe objects are determined as described above on the basis of thetransducer locations thus determined and of the sensed directions to theobjects OB₁ OB₃.

For the sake of simplicity only four markers are shown in FIG. 3a.However, the stand is preferably provided with more markers than shownto enable the location of the transducer to be reliably determined,preferably independently of its orientation and of its location in thestand. Markers may be applied in each corner and midway on each side ofthe stand, for instance (see FIG. 3b). The markers may also be ofdifferent types in order to supply more information.

The stand CF may be in the form of a frame of metal sections or rodswith suitable reinforcement, e.g. in the form of diagonals or cornerplates, so that the positions of the markers in relation to each otherare maintained with sufficient accuracy. The stand is preferablyparallel-epipedic in shape and, according to a preferred embodiment, iscollapsible and portable. When the required markers have been placedout, or other suitable objects have been defined, the stand is placed ina suitable place in relation to the objects/markers and the measurementis performed. The stand can then be removed and the transducer equipmentthereafter makes use of the determined objects.

A stand of the type described can be used not only for measurement inthe manner described but also during operation of a transducerequipment. The work space of the transducer then consists substantiallyof the interior of the stand and, during operation, the transducer usesthe stand's own markers. The shape and dimensions of the stand areadjusted to the application so that the transducer equipment and anyarrangements supporting it (e.g. an industrial robot) can operate freelywithin a sufficiently large work space. A transducer equipment can thusbeing taken into operation very quickly and imply by unfolding the standand placing it in the desired place. The same is applicable to movingits work space, in which case the stand is simply moved to the new site.In this application, the stand does not necessarily have to have a clearview of external objects.

FIG. 3b shows an embodiment of the stand CF described above. It consistsof a parallel-epipedic box with open sides. The box may be made of metalor plastic, for instance. According to one embodiment it consists of thebox in which the transducer equipment was packed upon delivery. The boxmay be made of cardboard with markers already printed on the inside andwith tear indications enabling removal of those parts of the sidesurfaces that shall be open. The positions of the markers in relation toeach other may be pre-programmed in the transducer equipment. Thisembodiment enables a transducer equipment to be taken into operation, orits work space to be moved, extremely simply and quickly.

FIG. 3c shows an example of how a marker may be arranged inside thestand, midway on one of its sides CF1. The marker is in the shape of asmall filled circle M₁₀ a with a surrounding circle M₁₀ b. It mayconsist of reflecting paint or tape for illumination by a light sourceapplied on the transducer. It may possibly consist of fluorescent paintfor illumination by an ultraviolet light source. If the stand is in theform of a cardboard box, the marker may be printed or applied on the boxat the time of manufacture. This also applies to markers arranged in thecorners.

FIG. 3d shows how a marker M₅ may alternatively be arranged on a tab CF2of the box material. The tab forms part of the bottom of the box duringmanufacture and is provided with tear indications along three sides. Thetab is folded up along its fourth side against the vertical part of theside CF1 and attached to this, e.g. by tape or by being inserted into apre-punched slit in the side CF1.

The structures described above with reference to FIGS. 3a-3d, carryingthe reference markers M₁, M₂ etc. are only a few of many feasibleembodiments of such a structure. The structure letting through therelevant signals may alternatively consist of a globe or other containerhaving walls of material pervious to the relevant wavelength band (suchas glass or plastic in the case of optical signals) and where thereference markers may consist of markers or reflecting tape applied onthe inside of the walls.

The structures described above with reference to FIGS. 3a-3d consist offrames with parallel-epipedic shape. Of course, the structures need notbe parallel-epipedic in shape but may be in the shape of any regular orirregular polyhedron.

FIG. 4a shows a rectangular beam TB with two transducer locations. Atransducer G may be placed in either of the transducer locations. Theseare so shaped that the location of the transducer in each transducerlocations is carefully defined in relation to the beam. The transducermay thus assume the locations P₁ and P₂, which are accurately known inrelation to each other. When performing a-measurement with thetransducer in one of the transducer locations, e.g. P₁, the directionsto the objects OB₁ -OB_(n) are determined first. Then, without alteringthe position or orientation of the beam, the same thing is performedwith the transducer in location P₂. Thus the directions of the sightlines for each object are known from two separate locations, which arein turn known in relation to each other since they are defined by thetransducer locations in the beam. As is clear from the description abovewith reference to FIGS. 1 and 2, this enables determination of thepositions of the objects. These positions will admittedly be determinedin the coordinate system of the beam, which is of no interest. However,since the positions of the objects are known in a coordinate system, thepositions of the objects in relation to each other are also known. Theuse of a transducer system requires knowledge of these relativepositions, and the relative positions are independent of in whichcoordinate system the absolute positions are determined.

The beam TB in FIG. 4a is shown only schematically. It may be designedin many ways, such as in the form of a rod or a metal section with aholder for a transducer at each end. Alternatively, the beam TB may beprovided with two transducers, one in each transducer location.Coordinating the measurements between the two transducers allowselimination of the requirement of not moving the beam.

The arrangement described here can be provided with more than twotransducers or transducer locations. It may, for instance, be in theform of a triangular frame with three transducer locations. Similarly,the beam or frame may be provided with two or more transducers ortransducer locations directed in different directions in order to givegreater freedom in orienting the beam/frame.

The arrangement may be in the form of an integrated and e.g. hand-heldtransducer unit with two or more transducers. Such a transducer unit canbe made auto-determining new objects'positions. A transducer unit ofthis type is shown in FIG. 4b. It has a central part 12 shaped so thatit can be held comfortably in the hand. Direction-sensing sensors 11aand 11b of previously described type are provided at each end. Thesensors are angled in relation to each other, or they may be parallel(as in FIG. 4a) or oppositely directed.

In the same way as described with reference to FIG. 3 the measuringaccuracy can be greatly increased by performing a plurality ofmeasurements with the beam in different locations. FIG. 5 shows atransducer G which, when in operation, makes use of a set OSA of objects(OBA₁, OBA₂ . . . ), the positions of which are known, e.g. by theobjects having previously been determined in one of the ways describedabove. When extending the working range the objects can be used fordetermining the positions of a set OSB of new objects (OBB₁, OBB₂ . . .). In principle, this can be performed in the manner described withreference to FIGS. 1-3, i.e. in each of a plurality of (at least two)separate transducer locations (P₁ and P₂ in FIG. 5) the transducer'slocation is determined with the aid of the known objects OSA and alsothe directions to the objects in the set OSB, after which the positionsof the objects in set OSB are calculated in the manner described.

As is clear from the above, the invention offers a method to determinethe positions of objects with unknown positions to be performed quicklyand simply with great accuracy, without the need for any measuringequipment other than the transducer equipment which is to make use ofthe determined objects, possibly supplemented by a simple mechanicalstructure.

What is claimed is:
 1. A method of determining positions of objects (OB₁-OB_(n), OSB) in equipment to determine the position or orientation of atransducer with the aid of a set of objects (OB₁ -OB_(n), M₁ -M_(n),OSA, OSB), which are arranged to emit signals that propagate linearlybetween the objects and the transducer, said equipment having thetransducer (G) designed to receive signals being emitted by objects insaid set, means arranged to produce direction-defining signals thatdefine directions in relation to the transducer, of the sight lines fromthe transducer to the objects, and calculation means arranged, on thebasis of the signals that define the direction to a number of objects(M₁ -M_(n), OSA) with known positions in relation to each other, togenerate information defining the position or orientation of thetransducer, the method comprisingdetermining for each of the objects(OB₁ -OB_(n), OSB) to be positionally determined, the directions of thesight lines to the object with the aid of the transducer (G) from atleast two separate transducer locations (P₁, P₂) known in relation toeach other, determining at least certain transducer locations (P₁, P₂)with the aid of a plurality of reference objects (M₁ -M_(n), OSA) withknown positions in relation to each other, wherein the transducerlocations are calculated from the positions of the reference objects andfrom the directions sensed by the transducer of the sight lines from thetransducer to the reference objects, calculating, for the objects to bepositionally determined, a measurement of the position (v_(i)) ororientation of the object from the said transducer locations (P₁, P₂)and from the directions (k_(ij)) to the object determined with the aidof the transducer.
 2. The method as claimed in claim 1, wherein aholding device (CF) carrying the reference objects is used during thedetermination of objects.
 3. The method as claimed in claim 2, whereinthe holding device is three-dimensional and is used during themeasurement, and that the transducer locations are selected so that atleast certain of the transducer location are situated within the holdingdevice.
 4. The method as claimed in claim 1, wherein the transducer usedin the determination process is carried by hand.
 5. An arrangement forcreating a set of objects with known positions for equipment todetermine the position or orientation of a transducer with the aid of aset of objects (OB₁ -OB_(n), M₁ -M_(n), OSA, OSB), which are arranged toemit signals that propagate linearly between the objects and thetransducer, said equipment havinga transducer (G) designed to receivesignals being emitted by objects in said set, means arranged to producedirection-defining signals that define the direction in relation to thetransducer, of the sight lines from the transducer to the objects,calculation means arranged, on the basis of the signals that define thedirections to a number of objects (M₁ -M_(n), OSA), with known positionsin relation to each other, to generate information defining the positionor orientation of the transducer, and, a mechanical structure (CF) witha plurality of reference objects (M₁ -M_(n)), whose positions inrelation to each other are known, is carried by the structure todetermine the position or orientation of the transducer.
 6. Thearrangement as claimed in claim 5, wherein the mechanical structureconsists of a frame.
 7. The arrangement as claimed in claim 6, whereinthe mechanical structure is three-dimensional and has reference objects(M₁ -M_(n)) facing the interior of the structure, the structure and thereference objects being so arranged that the transducer can be arrangedin a plurality of separate transducer locations within the structure. 8.The arrangement as claimed in claim 6, wherein the mechanical structureis designed to be portable.
 9. The arrangement as claimed in claim 6,wherein the mechanical structure is in the form of a polyhedron.
 10. Thearrangement as claimed in claim 5, wherein the mechanical structure isthree-dimensional and has reference objects (M₁ -M_(n)) facing theinterior of the structure, the structure and the reference objects beingso arranged that the transducer can be arranged in a plurality ofseparate transducer locations within the structure.
 11. The arrangementas claimed in claim 10, wherein the mechanical structure is designed tobe portable.
 12. The arrangement as claimed in claim 10, wherein themechanical structure is in the form of a polyhedron.
 13. The arrangementas claimed in claim 5, wherein the mechanical structure is designed tobe portable.
 14. The arrangement as claimed in claim 13, wherein themechanical structure is in the form of a polyhedron.
 15. The arrangementas claimed in claim 5, wherein the mechanical structure is in the formof a polyhedron.
 16. A method of determining positions of objects (OB₁-OB_(n), OSB) in equipment to determine the position and orientation ofa transducer with the aid of a set of objects (OB₁ -OB_(n), M₁ -M_(n),OSA, OSB), which are arranged to emit signals that propagate linearlybetween the objects and the transducer, said equipment having thetransducer (G) designed to receive signals being emitted by objects insaid set, means arranged to produce direction-defining signals thatdefine directions in relation to the transducer, of the sight lines fromthe transducer to the objects, and calculation means arranged, on thebasis of the signals that define the direction to a number of objects(M₁ -M_(n), OSA) with known positions in relation to each other, togenerate information defining the position or orientation of thetransducer, the method comprisingdetermining for each of the objects(OB₁ -OB_(n), OSB) to be positionally determined, the directions of thesight lines to the object with the aid of the transducer (G) from atleast two separate transducer locations (P₁, P₂) known in relation toeach other, determining at least certain transducer locations (P₁, P₂)with the aid of a plurality of reference objects (M₁ -M_(n), OSA) withknown positions in relation to each other, wherein the transducerlocations are calculated from the positions of the reference objects andfrom the directions sensed by the transducer of the sight lines from thetransducer to the reference objects, calculating, for the objects to bepositionally determined, a measurement of the position (v_(i)) andorientation of the object from the said transducer locations (P₁, P₂)and from the directions (k_(ij)) to the object determined with the aidof the transducer.
 17. The method as claimed in claim 16, wherein aholding device (CF) carrying the reference objects is used during thedetermination of objects.
 18. The method as claimed in claim 17, whereinthe holding device is three-dimensional and is used during themeasurement, and that the transducer locations are selected so that atleast certain of the transducer locations are situated within theholding device.
 19. The method as claimed in claim 16, wherein thetransducer used in the determination process is carried by hand.
 20. Anarrangement for creating a set of objects with known positions forequipment to determine the position and orientation of a transducer withthe aid of a set of objects (OB₁ -OB_(n), M₁ -M_(n), OSA, OSB), whichare arranged to emit signals that propagate linearly between the objectsand the transducer, said equipment havinga transducer (G) designed toreceive signals being emitted by objects in said set, means arranged toproduce direction-defining signals that define the direction in relationto the transducer, of the sight lines from the transducer to theobjects, calculation means arranged, on the basis of the signals thatdefine the directions to a number of objects (M₁ -M_(n), OSA), withknown positions in relation to each other, to generate informationdefining the position and orientation of the transducer, and, amechanical structure (CF) with a plurality of reference objects (M₁-M_(n)), whose positions in relation to each other are known, is carriedby the structure to determine the position or orientation of thetransducer.
 21. The arrangement as claimed in claim 20, wherein themechanical structure consists of a frame.
 22. The arrangement as claimedin claim 21, wherein the mechanical structure is three-dimensional andhas reference objects (M₁ -M_(n)) facing the interior of the structure,the structure and the reference objects being so arranged that thetransducer can be arranged in a plurality of separate transducerlocations within the structure.
 23. The arrangement as claimed in claim21, wherein the mechanical structure is designed to be portable.
 24. Thearrangement as claimed in claim 21, wherein the mechanical structure isin the form of a polyhedron.
 25. The arrangement as claimed in claim 20,wherein the mechanical structure is three-dimensional and has referenceobjects (M₁ -M_(n)) facing the interior of the structure, the structureand the reference objects being so arranged that the transducer can bearranged in a plurality of separate transducer locations within thestructure.
 26. The arrangement as claimed in claim 25, wherein themechanical structure is designed to be portable.
 27. The arrangement asclaimed in claim 25, wherein the mechanical structure is in the form ofa polyhedron.
 28. The arrangement as claimed in claim 20, wherein themechanical structure is designed to be portable.
 29. The arrangement asclaimed in claim 28, wherein the mechanical structure is in the form ofa polyhedron.
 30. The arrangement as claimed in claim 20, wherein themechanical structure is in the form of a polyhedron.